CAIE A-Level Mathematics AS 1.3.3 Circle Equation Questions

Practise reading a circle's centre and radius, completing squares in expanded equations and forming circle equations from centres, points, diameters or geometric constraints.

Exam points

apply coordinate geometry methods
solve coordinate geometry problems
interpret geometric results

[Maximum number: 2]

Figure for Question CAIE A-Level Mathematics AS 1.3.3 Circle Equation Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the circle with centre C(-4,5) and radius $\sqrt{20}$ units. The circle intersects the y-axis at the points A and B. The size of angle A C B is $\theta$ radians.

Find the equation of the circle in the form $x^{2}+y^{2}+a x+b y+c=0$ .

State or imply $(x+4)^{2}+(y-5)^{2}=20$
If $x^{2}+y^{2}-2 g x-2 f y+c=0$ is used correctly with
(-g,-f)=(-4,5) and $c=g^{2}+f^{2}-r^{2}$ then M1.

Obtain $x^{2}+y^{2}+8 x-10 y+21=0$
A1 if above method used.

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CAIE A-Level Mathematics AS 1.3.3 Circle Equation Questions question 1